Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  z1' : list A
  z1 : list B
  z : All2 (λ (x : A) (y : B), R x (g x y)) z1' z1
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := z1'; pr2 := z1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))

  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 (g x0 y0)
  z : All2 (λ (x : A) (y : B), R x (g x y)) l l'
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} =
    {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))

  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 (g x0 y0)
  z : All2 (λ (x : A) (y : B), R x (g x y)) l l'
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} =
    {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))

  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 (g x0 y0)
  z : All2 (λ (x : A) (y : B), R x (g x y)) l l'
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} =
    {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))

  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 (g x0 y0)
  z : All2 (λ (x : A) (y : B), R x (g x y)) l l'
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} =
    {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))

  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         All2 (λ (x : A) (y : B), R x (g x y)) xs l'
         → All2 R xs (map2 g xs l')
  y : B
  ys : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 (g x0 y0)
  z : All2 (λ (x : A) (y : B), R x (g x y)) l l'
  ============================
   ({| pr1 := x :: xs; pr2 := y :: ys |} =
    {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 R xs (map2 g xs ys))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim